Math Is Fun Forum

Dylan D.

Guest

Floor and Ceiling

Let f(x) = floor of \frac{2-3x}{x+5}. Find f(1)+f(2)+f(3)...+f(999)+(1000).

Suppose that |a - b| + |b - c| + |c - a| = 20. What is the maximum possible value of |a - b|?

Suppose that |a - b| + |b - c| + |c - d| + \dots + |m-n| + |n-o| + \cdots+ |x - y| + |y - z| + |z - a| = 20. What is the maximum possible value of |a - n|?

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Floor and Ceiling

Hi;

you have to put LaTeX between

tags.

Last edited by ShivamS (2014-05-21 13:56:45)

harrychess

Member

Registered: 2014-04-04

Posts: 33

Re: Floor and Ceiling

So it would be

?

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Floor and Ceiling

Yes. For example, his post would be:

Let f(x) = floor of

Suppose that

. What is the maximum possible value of

?
Suppose that

. What is the maximum possible value of

?

For the code, click the "Quote" button on the bottom right hand side of my post.

Last edited by ShivamS (2014-05-21 14:04:05)

harrychess

Member

Registered: 2014-04-04

Posts: 33

Re: Floor and Ceiling

found that out... ok

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Floor and Ceiling

Hi Dylan;

Let f(x) = floor of \frac{2-3x}{x+5}. Find f(1)+f(2)+f(3)...+f(999)+(1000).

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

harrychess

Member

Registered: 2014-04-04

Posts: 33

Re: Floor and Ceiling

So... how are you supposed to work these type of problems?

harrychess

Member

Registered: 2014-04-04

Posts: 33

Re: Floor and Ceiling

Hi Dylan;

Let f(x) = floor of \frac{2-3x}{x+5}. Find f(1)+f(2)+f(3)...+f(999)+(1000).

Sorry, I gave you the problem with a typo. It should be f(1000).

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Floor and Ceiling

Let f(x) = floor of \frac{2-3x}{x+5}. Find f(1)+f(2)+f(3)...+f(999)+f(1000)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

harrychess

Member

Registered: 2014-04-04

Posts: 33

Re: Floor and Ceiling

How are you supposed work do the other two problems?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Floor and Ceiling

I am working on them using a generating function approach but no luck yet.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.